Tunable filter

A tunable filter comprising:

• a piezoelectric resonator;
• an inductance for band extension connected to the piezoelectric resonator;
• a variable capacitance connected to the piezoelectric resonator;
• an input terminal;
• and
• an output terminal;
• wherein
• the tunable filter uses Love waves;
• the piezoelectric resonator includes a LiNbO3 substrate and an interdigital transducer (IDT) electrode provided on the LiNbO3 substrate;
• a pass band and an attenuation region are present in a frequency region on a lower frequency side relative to a value obtained by a calculation in which an acoustic velocity of a low-velocity transversal wave propagating in the LiNbO3 substrate is divided by a wave length defined by a period of the IDT electrode;
• the piezoelectric resonator includes a first piezoelectric resonator that includes an elastic wave resonator and is provided in a serial arm that connects the input terminal to the output terminal, and a second piezoelectric resonator that includes an elastic wave resonator and is provided in a parallel arm that connects the serial arm to a ground potential;
• the inductance for band extension includes a first inductance that is connected to the first piezoelectric resonator and extends a relative band of the first piezoelectric resonator, and a second inductance that is connected to the second piezoelectric resonator and extends a relative band of the second piezoelectric resonator;
• the variable capacitance includes a first variable capacitance that is connected to the first piezoelectric resonator and defines a first variable resonance circuit along with the first piezoelectric resonator and the first inductance, and a second variable capacitance that defines a second variable resonance circuit along with the second piezoelectric resonator and the second inductance;
• and
• the IDT electrode includes a Pt film, and in a case where a film thickness of the Pt film is taken as H(λ) and Euler angles of the LiNbO3 substrate are taken as (φ, θ, ψ), θ falls within a range of −64960×H3+19831×H2−2068.4×H+169.7−10° to −64960×H3+19831×H2−2068.4×H+169.7+6°, φ falls within a range of −27° to +27°, and ψfalls within a range of −47° to +47°.

A tunable filter comprising:

• a piezoelectric resonator;
• an inductance for band extension connected to the piezoelectric resonator;
• and
• a variable capacitance connected to the piezoelectric resonator;
• wherein
• the tunable filter uses Love waves;
• the piezoelectric resonator includes a LiNbO3 substrate and an interdigital transducer (IDT) electrode provided on the LiNbO3 substrate;
• a pass band and an attenuation region are present in a frequency region on a lower frequency side relative to a value obtained by a calculation in which an acoustic velocity of a low-velocity transversal wave propagating in the LiNbO3 substrate is divided by a wave length defined by a period of the IDT electrode;
• and
• in a case where a thickness of the IDT electrode is taken as H(λ) and a ratio P/PPt of a density P of the IDT electrode to a density PPt of Pt is taken as A, among the Euler angles (φ, θ, ψ), θ falls within a range of −64960×(H/A)3+19831×(H/A)2−2068.4×H/A+169.7−10° to −64960×(H/A)3+19831×(H/A)2−2068.4×(H/A)+169.7+6°, φ falls within a range of −27° to +27°, and ψ falls within a range of −47° to +47°.